Registration of optical images of turbid media

ABSTRACT

A co-registration system provides a means for spatially warping an optical image of an object with another images of a similar object. The optical image may be a scatter image, and the second image may be the same type of image modality, or may be different. The co-registration may use landmarks selected by a user, or may make use of contour information derived from the images. The system may also include processing of three-dimensional volume data in the form of sets of two-dimensional slices for co-registration.

FIELD OF THE INVENTION

This application relates to optical imaging of turbid media such asbreast tissue that is to be combined or used with other optical imagingof the same media.

BACKGROUND OF THE INVENTION

Optical imaging can provide valuable information about turbid media suchbiological tissue. Recent developments in both hardware and softwareenable rapid acquisition and processing of optical data to generateoptical images of tissues. The use of optical imaging of living tissue,such as breast, brain or whole body of small animals, is growing withinthe medical and pharmaceutical research communities. Its advantages overother imaging modalities, such as X-ray, ultrasound, PET or SPECT andMRI, is that it can provide rich optical spectrum analytical informationabout tissue composition and that the imaging is done using non-ionizingradiation (i.e. light) without any adverse effect on tissue. Forexample, chromophore information can help discern between oxygenated anddeoxygenated blood that is quite useful to understand the functionwithin the tissue. In some cases, an exogenous marker, whetherfluorescent or a chromophore, may be injected into the tissue to aid inlocalizing or visualizing objects of interest. Markers can selectivelyattach to certain molecules within tissue and the concentration of amarker within tissue can reveal important information about the state ofthe tissue.

Because tissue is a turbid medium, namely it scatters light heavily,optical imaging is a challenge. Optical scatter in tissue largelyresults from changes in the index of refraction caused by cellular andintracellular boundaries. Injected light thus becomes a diffuse glowwhen detected either at the other side of the tissue in transmissionmode or at the same side of the tissue in reflection mode. In theimaging process, scattering of light within the tissue must be accountedfor correctly if imaging with good spatial resolution is to be achieved.When light is injected into tissue, it is scattered and absorbed. Thecombination of the scattering and absorption of the light provides theoverall attenuation of light between source and detector. In the case ofa fluorophore, the absorbed light may be reemitted at a wavelength andtime that varies as a function of the fluorophore properties.

Optical scatter, namely the density and level of contrast of index ofrefraction boundaries within tissue, is generally a source of structuralinformation. However, since the absorption and/or the fluorescentreemission is a source of biological information of interest that is notobtainable with X-ray imaging, and since the location within the tissueof this biological information is to be identified, optical scatter isdetermined within the imaging process to allow for proper spatialidentification of concentration of fluorophore and/or chromophoreconcentrations. Generally, scatter information is obtained by acquiringtime dependent optical information, namely through time domain orfrequency domain optical data acquisition.

SUMMARY OF THE INVENTION

In accordance with the present invention, a system and method areprovided for performing a co-registration between a first image of anobject derived from optical scanning and a second image of an objectderived from optical scanning or some other scanning modality. Theco-registration uses certain features that are identified in each of thetwo images. The term co-registration referred to herein, means a warpingfunction that assigns points of an image to points of another image in arealistic way, i.e., such that features in one image corresponds to thesame features in the other image. The two images may be images ofdifferent, but similar, regions of tissue, or they may be the sameregion of tissue imaged at different times.

The co-registration system includes a database in which image data isstored. A user interface is provided by which a user may view the imagesand identify relevant points in each image. A co-registration moduleuses the image data and the identified points to co-register the images,and to provide an output indicative of a result of the co-registration.

In a first embodiment of the invention, the co-registration module useslandmarks in the images themselves to build the correspondence betweenthe two images. The landmarks may be selected by the user and identifiedvia the user interface, and may be notable features of the object thatare visible in the images, such as specific optical scatter patterns ina scatter image. The landmarks may also be selected automatically fromcomponents of the images based on predetermined selection criteria. Thelandmarks may be changed or deleted after viewing of the co-registrationmodule output, and additional multiple sets of landmarks may be storedfor the same two images.

In a second embodiment of the invention, the co-registration module usescontour data derived from the images. In one example, the contourrepresents an outer surface of the object. When using image data from anoptical imaging system that immerses the object in an optical matchingfluid, a first image of the object may be taken of the object in theabsence of the matching fluid. This provides an image with a clearerindication of the contour. The contour may be determined automatically,or with the assistance of a user via the user interface. Theco-registration module thereafter co-registers the images using thecontour data.

The system may also include an image data processing module thatoperates on three-dimensional image data to produce two-dimensionalimages. The module slices the data volume along parallel planes tocreate sets of two-dimensional image planes that each represent an imagevolume. The co-registration may thereafter proceed by operating on eachslice of a volume.

In one variation of the invention, an optical image representsabsorption data from a scan of an object, that is, a distribution of anabsorption coefficient. In another variation, the image may include dataregarding luminescence from fluorescent or phosphorescent regions of theobject.

In one particular use of the invention, the imaged object may be a humanbreast. In such a use, an optical image may be registered with anoptical image of a different breast, or with an optical image of thesame breast taken at a different time. An optical image of the breastmay also be registered with an image of the breast acquired usinganother modality, such as X-ray.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood by way of the following detaileddescription with reference to the appended drawings in which:

FIG. 1 is a schematic block diagram of an optical image co-registrationsystem;

FIGS. 2A and 2B depict a first set of comparative optical images showinga set of fiducial markers as used with the system of FIG. 1;

FIGS. 3A and 3B depict a second set of comparative optical imagesshowing a set of fiducial markers as used with the system of FIG. 1;

FIGS. 4A and 4B are a side view and a top view, respectively, of apatient's breast positioned in an optical scanner that may be used withthe system of FIG. 1; and

FIGS. 5A and 5B are schematic depictions, respectively, of a contourtaken from an X-ray image and a contour taken from an optical image foruse with the system of FIG. 1.

DETAILED DESCRIPTION OF THE INVENTION

Shown in FIG. 1 is a schematic block diagram of a system that may beused for performing a co-registration of two images. The systemcomprises a database 10 that contains image data, both in raw form andafter being processed. In this embodiment, the source of the raw data isscanner system 12. The scanner system is an optical imaging system suchas the optical breast imaging system sold under the name SOFTSCAN® byART Advanced Research Technologies Inc., St-Laurent, QC, Canada.However, those skilled in the art will recognize that the scanner systemmay be any of a number of different types of optical image systems. Alsostored in the database 10 are image data from external image sources 14,such as X-ray images, ultrasound images, or optical images from othersources. In addition, the database may store landmark and contour pointsprovided via a user console 16 that includes a display 18 and a userinterface 20. If the database is storing information regarding scans ofhuman patients, the data may be categorized by patient and by scan, asone patient may have different sets of data from scans that occurred atdifferent times. Of course, the system is equally applicable to theco-registration of scans from non-human tissue.

The console 16 allows a user to view images stored in the database 10and select landmarks or contour points to be used subsequently duringco-registration. Such landmark or contour points may be defined by auser viewing maps of the optical parameters, such as the modifiedscattering coefficient, that result from a scan. Previousco-registration results may also be viewed by a user who thereaftermodifies the landmark or contour points selected. The user may store theselected landmark or contour information in the database as part of thedata belonging to a selected scan. The interface also allows the storingof more than one set of selected points for a particular image, as wellas the deleting and changing of sets of points.

The system of FIG. 1 operates on optical image data, and doesco-registration of that image data with the data from other opticalimages, or from images generated by other modalities, such as X-ray.Likewise, images of fluorophore concentrations, generated by detectinglifetimes of specific fluorophores, may be co-registered. The processingof the raw optical data into an image may be performed by the scanningequipment, such as that of the system mentioned above, and theco-registration system of the present invention may operate as asubsystem, or as a separate standalone system, using image data from anysource.

In operation, the co-registration system of FIG. 1 allows the user toselect two sets of data, and perform co-registration between the data ofthe two sets. The co-registration makes use of a co-registration module22 that computes spatial transformation based on selected landmarkpoints or contour points. The module applies transformations to map eachset of data into the other. The result of the co-registration may thenbe displayed to a user in different ways via display 18.

One embodiment of the invention allows the co-registration of imagesusing landmark points in the images that are selected by a user based ona visual inspection of the images. FIGS. 2A and 2B and FIGS. 3A and 3B,show comparative optical images of the two breasts of a human patient.FIGS. 2A and 2B show the right and left breasts, respectively, imaged ona first occasion. FIGS. 3A and 3B show the same two breasts imaged atanother time. These images are scatter images (i.e., based on thereduced scattering coefficient μ_(s)′ for a specific wavelength) and, ineach of the figures, landmarks are indicated, and have been numberedfrom 0 to 5. These landmarks are selected by a user via interface 18after viewing the images on display 18 (FIG. 1). In this type of breastimaging, the compression of the breast, the angle of planar compressionand the water retention of the breast tissue are all factors that cancause the image of the same breast to change over a short period of timebetween image acquisitions.

In some optical images, such as scatter images, patterns inherent to thephysiological structures of the breast are very noticeable. Thesestructures may be different from breast to breast but tend to beconsistent in multiple images for the same breast. The patterns cantherefore be used to monitor the evolution of the breast over time andto evaluate, for example, how a diseased breast reacts to a chemicaltherapy. The present invention recognizes structural patterns such asthese and uses them as markers for co-registration.

An example of how a set of breast images may be analyzed for the purposeof co-registration is described below. In this example, the breast isscanned to provide a set of raw signal data (referred to as images)using an imaging system such as the SOFTSCAN® system described above. Intaking these images, the breast is compressed between two parallelplates. The three-dimensional image volumes are thereafter processedusing image data processing module 24. The structure in each of thepatient's two breast images is defined by a set of N landmark points. Inparticular, the volumes of the three-dimensional images are sliced alongZ-axis, perpendicular to the parallel plates compressing the breast,producing a set of effectively two-dimensional slices for each volume.The module 24 may also process multiple three-dimensional image volumesfor the same scan, where each of the volumes corresponds to a differentoptical wavelength used during the scan. In such a case, a different setof image slices for each of the different wavelengths may be generated.Slices may also be individually processed for different opticalproperties (e.g., absorption and scattering) or for differentphysiological indices. The processed data is returned from module 24 tothe database 10, where it is stored.

The image data from two images, A and B, are made available to theco-registration module 22 from the database 10. In this embodiment, themodule performs a co-registration based on landmark points, as indicatedat 22 a. For a given optical index, such as the scattering index, aparticular slice of the reconstructed volume of the breast isconsidered, the two-dimensional image data sets each corresponding toone of the three-dimensional images A and B. P and Q are used torepresent the sets of marker points defining structures in thetwo-dimensional images A and B, respectively, and may be represented asfollows:

P={(x ₁ ^(a) ,y ₁ ^(a)), (x ₂ ^(a) ,y ₂ ^(a)), . . . , (x _(N) ^(a) ,y_(N) ^(a))}

Q={(x ₁ ^(b) ,y ₁ ^(b)), (x ₂ ^(b) ,y ₂ ^(b)), . . . , (x _(N) ^(b) ,y_(N) ^(b))}

The co-registration of the two images can be expressed formally byfinding two functions ƒ and its inverse ƒ¹, such that:

(x ^(a) ,y ^(a))=ƒ(x ^(b) ,y ^(b)) and inversely (x ^(b) ,y ^(b))=ƒ⁻¹(x^(a) ,y ^(a))

where (x^(a), y^(a)) and (x^(b),y^(b)) denote the coordinates of a pointin image A and a point in image B respectively in such a way that, forany point of P and Q,

ƒ(x _(k) ^(b) ,y _(k) ^(b))εP and ƒ ⁻¹(x ^(a) _(k) ,y _(k) ^(a))εQ, withk=1 . . . N.

The manner in which computing functions ƒ and ƒ^(l) are derived dependson the number N. A minimum of three points will be used to do theco-registration, and the higher the number N, the more accurate theco-registration. The following table shows the type of well-knownfunctions that may be determined for a given minimum value for N.

Minimum N Type of function 3 ‘affine’ [u v] = [x y 1] * T T is a 3-by-2matrix and is obtained by solving the linear system of equations. 6‘Local Weighted Mean’ The method is described in paper: Goshtasby,Ardeshir, “Image registration by local approximation methods,” Image andVision Computing, Vol. 6, 1988, pp. 255-261

This co-registration technique is extended to the three-dimensionalvolume by applying the same geometrical transformation to each slice ofthe volume after repositioning the set of markers on the structures. Thefirst and the last slices may be ignored. The output of theco-registration module 22 may be stored in the database 10 and/orprovided to the user interface 16. The data output by theco-registration module may include look-up tables for warping image A toimage B, and vice versa.

It will be appreciated that once the optical scatter property image hasbeen registered with another image, an image of the absorptioncoefficient distribution is also registered since the optical dataacquisition intrinsically provides information regarding both themodified scatter coefficient and the absorption coefficient. Thus, oncethe registration of the images has been achieved with the scatteroptical image, all the other optical images available from the study(optical properties or physiological indices) can be displayed in aregistration mode, (i.e., after being warped).

The optical image may consist of a fluorescence image (meaning an imageincluding either fluorescence or phosphorescence image data). Thefluorescence (or “luminescence”) image can be generated by endogenous orexogenous molecules excited with an energy source such as light of anappropriate wavelength. The fluorescent images may be obtained by usingclinically approved fluorescent agents to tag specific tissue or tumors.

As mentioned above, the optical scatter image can be used to registeranother optical image of the same object taken at a different time. Thisis particularly advantageous when it is desired to follow the evolutionof the state of the object over time. For example, it may be desirableto follow the progression of a tumor in a breast (or other tissue)following treatment of the tumor.

The displayed result of the registration of the images may take severalforms. In one aspect, the optical image can be superimposed on the imageobtained by a different modality (because it was co-registered with theother method based on contour). Alternatively one of the images can bedisplayed with image annotations identifying features from the otherimage. In yet another embodiment a report can be generated with adescription of the characteristics of features and landmarks that haveco-registered in the two images.

In addition to performing co-registration using landmarks, it ispossible to perform co-registration using image contours. In thisalternative embodiment, points along a contour from the optical imageare used for co-registration with corresponding points from anotherimage. The contour typically represents the edges of the object beingimaged, which are clearly visible when using an image modality such asX-ray. However, in optical breast imaging, it may be more difficult tolocate the breast contour.

Using the SOFTSCAN® system described above, a breast being examined maybe positioned as is shown in FIGS. 4A and 4B (FIG. 4A being a side viewand FIG. 4B being a top view). In this type of breast imaging, thebreast is gently compressed between two plates 26. The plates aresubstantially parallel to each other to provide a rectangular geometry.One or more light sources 28 are coupled to one of the plates using, forexample, optical fibers. Detectors 30 are positioned on the other plate,thereby allowing acquisition of an optical signal in a transmissionmode. While the plates confer a generally rectangular shape to theobject, it can be appreciated from the top view and the cross-sectionalview that the edges 32 of the object are rounded, and not simple regularshapes.

For the purpose of breast imaging, a time domain multi-wavelength systemhaving a slab geometry with the breast pendant in a rectangular tanksurrounding by a scattering matching fluid can be used. In oneembodiment, a single source with five associated detectors is rasterscanned through the entire surface of the slab in increments of 3 mm.For each scan point, five detector positions are used in a transmissionmode. For a source located at (0, 0, 0), the corresponding detectorlocations may be, for example, Detector 1: (−25 mm, 5 mm, 60 mm),Detector 2: (25, 5, 60), Detector 3: (0, 0, 60), Detector 4: (−25, −15,60) and Detector 5: (25, −15, 60).

Because the matching fluid tends to obscure the contour of the breast inthe resulting optical image, the source and a central detector are firstused prior to filling the tank with the matching fluid. The source anddetector are operated in a “quasi-continuous wave (CW) mode” and providethe desired “breast contour image” (BCI) data. This BCI data is storedin the database (FIG. 1) with the rest of the data. The BCI is donethrough a raster scan of horizontal movements of a source-detector. Thesource emits a signal that is collected by the detector, and the signaldisappears at the edge of the breast. For that horizontal line of thescan, the system determines points where the signal disappears ascorresponding to the intersection of edge breast with the horizontalline of the scan. The points (generally two points) are put in the setof points defining the contour. Subsequently, the horizontal line of thescan is shifted to a different horizontal line, and the process repeats.

For this embodiment of the invention, the system performs aco-registration based on contour, as indicated at 22 b. The manner inwhich this co-registration is performed may be better understood fromFIGS. 5A and 5B. FIG. 5A shows the relevant contour from an X-ray image,while FIG. 5B shows the relevant contour from a corresponding opticalimage. The co-registration function P_(S)=f(P_(X)), where P_(S) is apoint in the optical image and P_(X) is a point in the X-ray image isconstructed in the following way:

-   -   a) First a user, who may be a radiologist or a physician,        defines two points in the X-ray image. The two points selected        in this example are: the nipple N_(X) and the chest-wall by        point C_(X). N_(X) and C_(X) are used to define a new reference        axis in the X-ray image, as shown in FIG. 5A.    -   b) In the optical image, these two points are defined        automatically. The nipple N_(S) can be defined as the lowest        point of the BCI. This rule is derived from the observation        that, for this type of optical system, the woman is lying        horizontally during the breast imaging scan and, thus, her        breast is in a pendant position. The other point C_(S) is        defined as the intersection of a vertical line from N_(S) to a        horizontal line defined by the extremities of the BCI.    -   c) A correspondence is built between the left part of the BCI,        defined from the nipple N_(S) and the left part of the X-ray        contour defined from the point N_(X),    -   d) Another correspondence is built in a similar way between the        right part of the BCI and the X-ray contour.    -   e) The ratio between the lengths of the medial axes will be used        first to define the lengths of left and right parts of X-ray        contour in the following way:

$R = \frac{{C_{X} - N_{X}}}{{C_{S} - N_{S}}}$

-   -   -   Right part of X-ray Contour=R*(Right part of the BCI).        -   Left part of X-ray Contour=R*(Left part of the BCI).

    -   This constrains only a small part of X-ray image being in        correspondence with the optical image. Points outside that        region are not regarded by the co-registration process and do        not have corresponding points in the optical image. Points in        the right region in optical image correspond to points in the        right region in X-ray image, and vice versa. The same applies        for left regions.

    -   f) Coordinates System: One may define H_(S) as the projection of        a point P_(S) on the line defined by points N_(S)C_(S) and H_(X)        as the projection of point P_(X) on the line defined by points        N_(S)C_(S). Similarly, Q_(S) is the intersection point between        line HsPs and the left or right BCI part, depending on which        side P_(S) is on. In the same way, let Q_(X) is the intersection        point between line H_(X)P_(X) and the left or right X-ray        contour part, depending on which side P_(X) is on. Then a point        P_(S) can be defined by its coordinates in the following way:

$P_{S} = \left\{ {{\begin{matrix}{a_{s} = \frac{{P_{S} - H_{S}}}{{Q_{s} - H_{s}}}} \\{b_{s} = \frac{{H_{S} - N_{s}}}{{C_{s} - N_{s}}}}\end{matrix}\mspace{14mu} {where}\mspace{14mu} 0} \leq b_{s} \leq {{1\mspace{14mu} {and}}\mspace{14mu} - 1} \leq a_{S} \leq 1} \right.$

-   -   In similar way a point in the X-ray image can be expressed as:

$P_{X} = \left\{ {{\begin{matrix}{a_{X} = \frac{{P_{X} - H_{X}}}{{Q_{X} - H_{X}}}} \\{b_{X} = \frac{{H_{X} - N_{X}}}{{C_{X} - N_{X}}}}\end{matrix}\mspace{14mu} {where}\mspace{14mu} 0} \leq b_{X} \leq {{1\mspace{14mu} {and}}\mspace{14mu} - 1} \leq a_{X} \leq 1} \right.$

-   -   g) The co-registration procedure consists of finding for any        point in optical image P_(S), a point P_(X) in the X-ray image        that has the exactly the same coordinates based on the        coordinate system described above.    -   h) Therefore in that system of coordinates, using the right part        of the contour for both modalities, are the set of points having        coordinates:

$P = \left\{ \begin{matrix}{a = 1} \\{B_{1} \leq b \leq 1}\end{matrix} \right.$

where boundary B₁≧0. In a similar way, using the left part of thecontour, there are the set of points

$P = \left\{ \begin{matrix}{a = {- 1}} \\{B_{2} \leq b \leq 1}\end{matrix} \right.$

where boundary B₂≧0. For both modalities, the nipple has the coordinates

$\left\{ {\begin{matrix}0 \\{0,}\end{matrix}\quad} \right.$

and the chest wall point has the coordinates

$\left\{ {\begin{matrix}0 \\1.\end{matrix}\quad} \right.$

This co-registration procedure ensures the following:

-   -   The nipple in the optical image corresponds to the nipple in the        X-ray image and vice-versa.    -   The point C_(X) corresponds to the point C_(S).    -   Points lying in the segment line N_(X)C_(X) are in        correspondence with points of the segment N_(S)C_(S)    -   Points in the right part of the contour of the optical image are        in correspondence with points lying in the right part of the        X-ray contour. Likewise, similar correspondence exists for the        left parts of BCI and the X-ray contour.    -   Points that are between the contour and the medial axis using        one modality are in correspondence with points that are between        the contour and medial axis using the other modality.

Generating an optical scattering data set.: Light propagation in tissueis well modeled by the diffusion equation. In the time domain themathematical expression modeling light propagation in a homogeneousmedium is:

$\begin{matrix}{{{{\frac{1}{v}\frac{\partial}{\partial t}{\Phi \left( {r,t} \right)}} - {D{\nabla^{2}{\Phi \left( {r,t} \right)}}} + {\mu_{a}{\Phi \left( {r,t} \right)}}} = {S\left( {r,t} \right)}},} & (1)\end{matrix}$

where Φ(r,t) is the photon flux, D=1/3μ′_(s) is the diffusioncoefficient expressed with μ′_(s) being the scattering coefficient,μ_(a) is the linear absorption coefficient, v is the speed of light inthe medium and s(r,t) is the source term (assumed to be a δ-function inour case). The temporal data acquired from a scan can be processed withdiffuse optical spectroscopy (DOS) and diffuse optical tomography (DOT).Many studies have been dedicated to solving equation (1) for diversegeometries. Delfino et al. (Delfino et al. Appl. Opt.(1999);38:4228-4236) suggested that, in the case of transmittance, theexpression provided by Contini et al. (Contini et al. Applied Optics(1997);36:4587-4599) results in the most satisfactory agreement betweenexperimental and theoretical predictions. In one embodiment of thepresent invention, the expression from Contini et al. can be used:

$\begin{matrix}{{{T\left( {\rho,t} \right)} = {\frac{\exp \left( {{{- \mu_{a}}{vt}} - \frac{\rho^{2}}{4{Dvt}}} \right)}{2\left( {4\pi \; {Dv}} \right)^{3/2}t^{5/2}}{\sum\limits_{m = {- \infty}}^{+ \infty}\begin{bmatrix}{{z_{1,m}{\exp \left( {- \frac{z_{1,m}^{2}}{4{Dvt}}} \right)}} -} \\{z_{2,m}{\exp \left( {- \frac{z_{2,m}^{2}}{4{Dvt}}} \right)}}\end{bmatrix}}}},} & (2)\end{matrix}$

where T(ρ,t) represents the probability that a photon, entering themedium at t=0, exits at a time t and at a distance ρ per unit of timeand unit of area. z_(1,m) and z_(2,m) are expressed by:

$\begin{matrix}\left\{ {{{{\begin{matrix}{{z_{1,m} = {{s\left( {1 - {2m}} \right)} - {4{mz}_{e}} - z_{o}}},} \\{z_{2,m} = {{s\begin{pmatrix}{1 -} \\{2m}\end{pmatrix}} - {\begin{pmatrix}{{4m} -} \\2\end{pmatrix}z_{e}} + z_{o}}}\end{matrix}m} = \left( {0,{\pm 1},{\pm 2},\ldots} \right)};{z_{o} = \frac{1}{\mu_{s}^{\prime}}}},} \right. & (3)\end{matrix}$

and account for the boundary conditions.

The theoretical expression of equation (2) is used in an inverse problemto retrieve the bulk optical properties of the medium underinvestigation. For example, a least squares fit can be performed withthree free parameters: the amplitude of the temporal point spreadfunction (TPSF), the absorption coefficient and the scatteringcoefficient. The best fit can be reached iteratively with aLevenberg-Marquardt algorithm and minimization of a χ² merit norm.

The absorption and scattering coefficients estimated through thisprocedure are related to the physiological and structural bulkproperties of the biological tissue probed. The absorption coefficientis related to the different constituents of the breast through thelinear contributions of the different tissue chromophores:

$\begin{matrix}{{\mu_{a}(\lambda)} = {\sum\limits_{i}^{NC}{ɛ_{i}^{\lambda}C_{i}}}} & (4)\end{matrix}$

where ε is the wavelength dependent extinction coefficient of the i^(th)chromophore and C its concentration. In the case of breast tissue, it iswidely assumed that the primary NIR absorbers are oxyhemoglobin,deoxyhemoglobin, hemoglobin, water and lipids (denoted as HbO₂, Hb, H₂Oand Li respectively). HbO₂ and Hb can be combined to obtain blood volume(HbT) and blood oxygen saturation (SaO₂). It will be appreciated thatother NIR chromophores (absorbers) can be present and that thecomposition of NIR chromophores may vary from tissue to tissue.

The scattering coefficient originates mainly from the refractive indexmicro-variations in tissue. It has been shown that a simpleMie-scattering approximation is applicable to scattering of breasttissue (Durduran et al. Phys Med Biol. (2002);47:2847-2861):

μ′_(s)(λ)=aλ ^(−b)  (5)

where a is referred to as scattering amplitude and b as scatteringpower. These last parameters are related to the breast composition.Typically, large scatterers have lower a and b values, whereas smallscatterers have higher a and b (Mourant et al. Appl. Opt.(1997);36:949-957). Moreover, Cerrusi et al. (Cerussi, Acad. Radiology2001; 8:211-218) show a linear relationship for both the lipid and watercontent to the scattering power. This relationship was establishedexperimentally from a study based on 28 women and with a coefficient ofdetermination r² of 0.84 for the lipid content and 0.85 for the watercontent. This relationship is expressed as:

[H ₂ O]=0.35*b−0.05(%)

[Li]=−0.50*b+0.90(%)  (6)

The accuracy of the time resolved technique can be used to obtainabsolute values of the scattering coefficient to estimate the lipid bulkconcentrations from equation (6). Then the inverse problem expressed inequation (4) is reduced to three chromophores and hence far betterconditioned. To solve equation (4) a non-negative least squares (NNLS)algorithm can be used. The initial value of the water concentration canbe provided by equation (6) but set as a free parameter in the fittingalgorithm.

It is also possible from multiple spatial measurements to estimate thelocal distribution of the absorption and scattering coefficients. Theconcept of this application is to employ measurements recorded fromtissue using multiple optical source—detector pairs and retrieve(reconstruct) the object function by synthesizing the measurementsthrough solution of an inverse problem (Arridge. Inverse problems(1999); 15: R41-R93).

One cost-efficient and robust approach to perform Diffuse OpticalTomography (DOT) is to solve the heterogeneous equation within the Rytovperturbative approach (O'Leary. PhD University of Pennsylvania 1996). Inthe case of time resolved measurements, there are potentially differenttypes of data sets. One can select the 0^(th) moment (equivalent tocontinuous mode) and 1^(st) moment (mean time of photon arrival) of theTPSF (Arridge. Inverse problems (1999);15:R41-R93). The DOT problem isthus expressed as:

$\begin{matrix}{\begin{bmatrix}{\Phi_{sc}^{(I)}\left( r_{{sd}\; 1} \right)} \\\vdots \\{\Phi_{sc}^{(I)}\left( r_{sdm} \right)} \\{\Phi_{sc}^{({MT})}\left( r_{{sd}\; 1} \right)} \\\vdots \\{\Phi_{sc}^{({MT})}\left( r_{sdm} \right)}\end{bmatrix} = {\begin{bmatrix}W_{11}^{(I)} & \ldots & W_{1n}^{(I)} \\\vdots & \ddots & \vdots \\W_{m\; 1}^{(I)} & \ldots & W_{mn}^{(I)} \\W_{11}^{({MT})} & \ldots & W_{1n}^{({MT})} \\\vdots & \ddots & \vdots \\W_{m\; 1}^{({MT})} & \ldots & W_{mn}^{({MT})}\end{bmatrix}\begin{bmatrix}{{\delta\mu}_{a}\left( r_{1} \right)} \\\vdots \\{{\delta\mu}_{a}\left( r_{n} \right)}\end{bmatrix}}} & (7)\end{matrix}$

where

${\Phi_{sc}^{(I)}\left( r_{sdi} \right)} = {\ln \left( \frac{U\left( r_{sdi} \right)}{U_{0}\left( r_{sdi} \right)} \right)}$

is the 0^(th) moment Rytov pertubation, Φ_(sc) ^((MT)) _(sdi)=t(r_(sdi))− t ₀(r_(sdi)) the 1^(st) moment Rytov perturbation, withW_(ij) ^((l)) and W_(ij) ^((MT)) the corresponding weight of thesensitivity matrix. The expressions for the weight functions are:

$\begin{matrix}{{W_{ij}^{(I)} = {\frac{1}{\left( {4\pi \; D} \right)^{2}r_{sivj}r_{vjdi}} \cdot {\exp \left\lbrack {{- \sqrt{\frac{\mu_{a}}{D}}} \cdot \left( {r_{sivj} + r_{vjdi}} \right)} \right\rbrack} \cdot \frac{1}{U_{0}\left( r_{sdi} \right)}}}{W_{ij}^{({MT})} = {{\frac{\left( {r_{sivj} + r_{vjdi}} \right)}{{c \cdot \sqrt{\mu_{a} \cdot D}}\left( {4\pi \; D} \right)^{2}r_{sivj}r_{vjdi}} \cdot {\exp \begin{bmatrix}{{- \sqrt{\frac{\mu_{a}}{D}}} \cdot} \\\begin{pmatrix}{r_{sivj} +} \\r_{vjdi}\end{pmatrix}\end{bmatrix}} \cdot \frac{1}{U_{0}\left( r_{sdi} \right)}} - \left( \frac{{{\overset{\_}{t}}_{0}\left( r_{sdi} \right)} \cdot W_{ij}^{(I)}}{U_{0}\left( r_{sdi} \right)} \right)}}} & (8)\end{matrix}$

with r_(sivj) and r_(vjdi), corresponding to the i^(th) source-j^(th)voxel and j^(th) voxel-i^(th) detector distances, respectively, andU₀(r_(sdi)) and t ₀ (r_(sdi)) correspond to the homogeneous 0^(th)moment and 1^(st) moment of the TPSF for the considered sourcedetector-pair.

It will be appreciated that other approaches can be used to derive thescatter “map” of an object as would be known by those skilled in theart.

While optical data acquisition has been described as applied to timedomain (TD), it will be appreciated that frequency domain (FD)acquisition may also be used to recover optical parameters such as μ_(a)and μ_(s)′. Algorithms for reconstruction in FD are well known in theart (Sevick-Muraca et al., Neoplasia 2: 388-417, 2000, incorporatedherein by reference).

While the invention has been described in connection with specificembodiments thereof, it will be understood that it is capable of furthermodifications and this application is intended to cover any variations,uses, or adaptations of the invention following, in general, theprinciples of the invention and including such departures from thepresent disclosures as come within known or customary practice withinthe art to which the invention pertains and as may be applied to theessential features herein before set forth, and as follows in the scopeof the appended claims.

1. A system for providing a co-registration between a first imagederived from an optical scanning of a object and a second image derivedfrom a scanning of an object with a configuration similar to the firstobject, the system comprising: a database in which image data is stored;a user interface that allows viewing of the images by a user andidentification of relevant points in the images viewed; and aco-registration module that receives a set of data points which identifycommon features of the first and second images, and that provides anoutput that enables a spatial warping of one of the images to the other.